The value of log 125 base root 5 is equal to 6, that is, log_{√5}125 = 6. In this post, we will learn how to find the logarithm of 125 when the base is √5.

## How to Find log125 Base Root 5

**Question:** What is log125 base√5?

**Answer:** log125 base root 5 equals 6.

**Solution:**

**Step 1:**

We know that 125 is a product of three numbers of 5’s. In other words, we can write 125 as follows.

125 = 5×5×5

⇒ 125 = 5^{3} …(∗)

Next, we write 5 as a power of √5.

5 = (√5)^{2}

Thus, Equation (∗) can be rewritten as

125 = [(√5)^{2}]^{3 }

∴ 125 = (√5)^{6 }by the indices rule a^{mn} = (a^{m})^{n}

**Step 2:**

Now, we will take logarithms with base √5 on both sides. This will give us

log_{√5}125 = log_{√5}(√5)^{6}

⇒ log_{√5}125 = 6 log_{√5}(√5)

⇒ log_{√5}125 = 6, as we know the logarithm formula: log_{a}a = 1.

Hence the value of log 125 base root 5 is 6.

**Have You Read These Logarithms?**

## FAQs

### Q1: What is log 125 with base root 5?

Answer: As 125=(√5)^{6}, the value of the log125 with base root 5 is equal to 6.